English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Generating functions for the univariate complex Hermite polynomials (UCHP)are employed to introduce some non-trivial one and two-dimensional integraltransforms of Segal-Bargmann type in the framework of specific functionalHilbert spaces. The approach used is issued from the coherent states framework.Basic properties of these transforms are studied. Connection to some specialknown transforms like Fourier and Wigner transforms is established. The firsttransform is a two-dimensional Segal-Bargmann transform whose kernel is relatedthe exponential generating function of the UCHP. The second one connects theso-called generalized Bargmann-Fock spaces (or also true-poly-Fock spaces inthe terminology of Vasilevski) that are realized as the $L^2$-eigenspaces of aspecific magnetic Schr\"odinger operator. Its kernel function is related to aMehler formula of the UCHP.

Non-trivial 1d and 2d integral transforms of Segal-Bargmann type